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        Functions  Reference
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                <a href="Functions.html#/s:15tulipindicators3absySi_SaySdGtACF">abs(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators5adosc_12short_period05long_D0Si_SaySdGtSayxG_S2dtAA8QuotableRzlF">adosc(_:short_period:long_period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3adx_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">adx(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators4adxr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">adxr(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators2aoySi_SaySdGtSayxGAA8QuotableRzlF">ao(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators3apoySi_SaySdGtACF">apo(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators8aroonosc_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">aroonosc(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators6arroon_6periodSi_AA12ArroonResultVtSayxG_SitAA8QuotableRzlF">arroon(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators4asinySi_SaySdGtACF">asin(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators4atanySi_SaySdGtACF">atan(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators3atr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">atr(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators8avgpriceySi_SaySdGtSayxGAA8QuotableRzlF">avgprice(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators6bbands_6period6stddevSi_AA11BBandResultVtSaySdG_SiSdtF">bbands(_:period:stddev:)</a>
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                <a href="Functions.html#/s:15tulipindicators3bopySi_SaySdGtSayxGAA8QuotableRzlF">bop(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators3cci_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">cci(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators4ceilySi_SaySdGtACF">ceil(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators3cmo_6periodSi_SaySdGtAD_SitF">cmo(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3cosySi_SaySdGtACF">cos(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators4coshySi_SaySdGtACF">cosh(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators8crossany1a1bSi_SaySdGtAE_AEtF">crossany(a:b:)</a>
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                <a href="Functions.html#/s:15tulipindicators9crossover1a1bSi_SaySdGtAE_AEtF">crossover(a:b:)</a>
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                <a href="Functions.html#/s:15tulipindicators3cvi_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">cvi(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators5decay_6periodSi_SaySdGtAD_SitF">decay(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators4dema_6periodSi_SaySdGtAD_SitF">dema(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators2di_6periodSi_AA9DirectionVtSayxG_SitAA8QuotableRzlF">di(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3divySi_SaySdGtACF">div(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators2dm_6periodSi_AA9DirectionVtSayxG_SitAA8QuotableRzlF">dm(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3dpo_6periodSi_SaySdGtAD_SitF">dpo(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators2dx_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">dx(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators6edecay_6periodSi_SaySdGtAD_SitF">edecay(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3ema_6periodSi_SaySdGtAD_SitF">ema(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3emvySi_SaySdGtSayxGAA8QuotableRzlF">emv(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators3expySi_SaySdGtACF">exp(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators6fisher_6periodSi_AA12FisherResultVtSayxG_SitAA8QuotableRzlF">fisher(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators5floorySi_SaySdGtACF">floor(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators3hma_6periodSi_SaySdGtAD_SitF">hma(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators4kama_6periodSi_SaySdGtAD_SitF">kama(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3kvo_5short4longSi_SaySdGtSayxG_S2itAA8QuotableRzlF">kvo(_:short:long:)</a>
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                <a href="Functions.html#/s:15tulipindicators3lag_6periodSi_SaySdGtAD_SitF">lag(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators6linreg_6periodSi_SaySdGtAD_SitF">linreg(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators15linregintercept_6periodSi_SaySdGtAD_SitF">linregintercept(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators11linregslope_6periodSi_SaySdGtAD_SitF">linregslope(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators2lnySi_SaySdGtACF">ln(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators5log10ySi_SaySdGtACF">log10(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators4macd_5short4long6signalSi_AA10MACDResultVtSaySdG_S3itF">macd(_:short:long:signal:)</a>
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                <a href="Functions.html#/s:15tulipindicators8marketfiySi_SaySdGtSayxGAA8QuotableRzlF">marketfi(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators4mass_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">mass(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3max_6periodSi_SaySdGtAD_SitF">max(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators2md_6periodSi_SaySdGtAD_SitF">md(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators8medpriceySi_SaySdGtSayxGAA8QuotableRzlF">medprice(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators3mfi_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">mfi(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3mom_6periodSi_SaySdGtAD_SitF">mom(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3msw_6periodSi_AA9MSWResultVtSaySdG_SitF">msw(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3mulySi_SaySdGtACF">mul(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators4natr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">natr(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3nvi_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">nvi(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3obvySi_SaySdGtSayxGAA8QuotableRzlF">obv(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators3ppo_5short4longSi_SaySdGtAE_S2itF">ppo(_:short:long:)</a>
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                <a href="Functions.html#/s:15tulipindicators4psar_12acceleration0C3MaxSi_SaySdGtSayxG_S2dtAA8QuotableRzlF">psar(_:acceleration:accelerationMax:)</a>
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                <a href="Functions.html#/s:15tulipindicators3pviySi_SaySdGtSayxGAA8QuotableRzlF">pvi(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators6qstick_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">qstick(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3roc_6periodSi_SaySdGtAD_SitF">roc(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators4rocr_6periodSi_SaySdGtAD_SitF">rocr(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators5roundySi_SaySdGtACF">round(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators3rsi_6periodSi_SaySdGtAD_SitF">rsi(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3sinySi_SaySdGtACF">sin(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators4sinhySi_SaySdGtACF">sinh(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators3sma_6periodSi_SaySdGtAD_SitF">sma(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators4sqrtySi_SaySdGtACF">sqrt(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators6stddev_6periodSi_SaySdGtAD_SitF">stddev(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators6stderr_6periodSi_SaySdGtAD_SitF">stderr(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators5stoch_7kPeriod08kSlowingC001dC0Si_AA11StochResultVtSayxG_S3itAA8QuotableRzlF">stoch(_:kPeriod:kSlowingPeriod:dPeriod:)</a>
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                <a href="Functions.html#/s:15tulipindicators8stochrsi_6periodSi_SaySdGtAD_SitF">stochrsi(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3sub1a1bSi_SaySdGtAE_AEtF">sub(a:b:)</a>
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                <a href="Functions.html#/s:15tulipindicators3sum_6periodSi_SaySdGtAD_SitF">sum(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3tanySi_SaySdGtACF">tan(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators4tanhySi_SaySdGtACF">tanh(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators4tema_6periodSi_SaySdGtAD_SitF">tema(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators5todegySi_SaySdGtACF">todeg(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators5toradySi_SaySdGtACF">torad(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators2trySi_SaySdGtSayxGAA8QuotableRzlF">tr(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators5trima_6periodSi_SaySdGtAD_SitF">trima(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators4trix_6periodSi_SaySdGtAD_SitF">trix(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators5truncySi_SaySdGtACF">trunc(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators3tsf_6periodSi_SaySdGtAD_SitF">tsf(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators8typpriceySi_SaySdGtSayxGAA8QuotableRzlF">typprice(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators6ultosc_5short6medium4longSi_SaySdGtSayxG_S3itAA8QuotableRzlF">ultosc(_:short:medium:long:)</a>
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                <a href="Functions.html#/s:15tulipindicators8variance_6periodSi_SaySdGtAD_SitF">variance(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3vhf_6periodSi_SaySdGtAD_SitF">vhf(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators5vidya_5short4long5alphaSi_SaySdGtAF_S2iSdtF">vidya(_:short:long:alpha:)</a>
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                <a href="Functions.html#/s:15tulipindicators10volatility_6periodSi_SaySdGtAD_SitF">volatility(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators4vosc_5short4longSi_SaySdGtSayxG_S2itAA8QuotableRzlF">vosc(_:short:long:)</a>
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                <a href="Functions.html#/s:15tulipindicators4vwma_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">vwma(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3wadySi_SaySdGtSayxGAA8QuotableRzlF">wad(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators7wcpriceySi_SaySdGtSayxGAA8QuotableRzlF">wcprice(_:)</a>
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                <a href="Functions.html#/s:15tulipindicators7wilders_6periodSi_SaySdGtAD_SitF">wilders(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators5willr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">willr(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators3wma_6periodSi_SaySdGtAD_SitF">wma(_:period:)</a>
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                <a href="Functions.html#/s:15tulipindicators5zlema_6periodSi_SaySdGtAD_SitF">zlema(_:period:)</a>
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            <a href="Protocols.html">Protocols</a>
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                <a href="Protocols/Quotable.html">Quotable</a>
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            <a href="Structs.html">Structures</a>
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                <a href="Structs/MSWResult.html">MSWResult</a>
              </li>
              <li class="nav-group-task">
                <a href="Structs/StochResult.html">StochResult</a>
              </li>
              <li class="nav-group-task">
                <a href="Structs/Tulip.html">Tulip</a>
              </li>
            </ul>
          </li>
        </ul>
      </nav>
      <article class="main-content">
        <section>
          <section class="section">
            <h1>Functions</h1>
            <p>The following functions are available globally.</p>

          </section>
          <section class="section task-group-section">
            <div class="task-group">
              <ul>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3sma_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/sma(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3sma_6periodSi_SaySdGtAD_SitF">sma(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Simple moving average</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">sma</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3wma_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/wma(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3wma_6periodSi_SaySdGtAD_SitF">wma(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Weighted moving average</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">wma</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3ema_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/ema(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3ema_6periodSi_SaySdGtAD_SitF">ema(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Exponential moving average</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">ema</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4dema_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/dema(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4dema_6periodSi_SaySdGtAD_SitF">dema(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Double exponential moving average</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">dema</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4tema_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/tema(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4tema_6periodSi_SaySdGtAD_SitF">tema(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Triple exponential moving average</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">tema</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5trima_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/trima(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5trima_6periodSi_SaySdGtAD_SitF">trima(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Triangular Moving Average</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">trima</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4kama_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/kama(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4kama_6periodSi_SaySdGtAD_SitF">kama(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Kaufman Adaptive Moving Average
/// - Parameter inputs: The inputs</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">kama</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators6bbands_6period6stddevSi_AA11BBandResultVtSaySdG_SiSdtF"></a>
                    <a name="//apple_ref/swift/Function/bbands(_:period:stddev:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators6bbands_6period6stddevSi_AA11BBandResultVtSaySdG_SiSdtF">bbands(_:period:stddev:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Compute the values of the three components
of the bollinger bands</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">bbands</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="nv">period</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">stddev</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="kt"><a href="Structs/BBandResult.html">BBandResult</a></span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>period</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>stddev</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The standard deviation</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                      <div>
                        <h4>Return Value</h4>
                        <p>The result as a tuple of (<code>Int</code> ,<code>BBBandResult</code>)</p>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3absySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/abs(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3absySi_SaySdGtACF">abs(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Absolute Value</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">abs</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4acosySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/acos(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4acosySi_SaySdGtACF">acos(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">acos</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators2adySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/ad(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators2adySi_SaySdGtSayxGAA8QuotableRzlF">ad(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Accumulation/Distribution Line</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">ad</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3add1a1bSi_SaySdGtAE_AEtF"></a>
                    <a name="//apple_ref/swift/Function/add(a:b:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3add1a1bSi_SaySdGtAE_AEtF">add(a:b:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector addition</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">add</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="nv">b</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>a</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>Inputs A</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>b</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>Inputs B</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5adosc_12short_period05long_D0Si_SaySdGtSayxG_S2dtAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/adosc(_:short_period:long_period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5adosc_12short_period05long_D0Si_SaySdGtSayxG_S2dtAA8QuotableRzlF">adosc(_:short_period:long_period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Accumulation/Distribution Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">adosc</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="nv">short_period</span><span class="p">:</span> <span class="kt">Double</span><span class="p">,</span> <span class="nv">long_period</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>short_period</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The short period value</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>long_period</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The long period value</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3adx_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/adx(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3adx_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">adx(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Average Directional Movement Index</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">adx</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>period</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4adxr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/adxr(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4adxr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">adxr(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Average Directional Movement Rating</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">adxr</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>period</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators2aoySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/ao(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators2aoySi_SaySdGtSayxGAA8QuotableRzlF">ao(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Aweosome Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">ao</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An arrayof <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3apoySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/apo(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3apoySi_SaySdGtACF">apo(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Absolute Price Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">apo</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators6arroon_6periodSi_AA12ArroonResultVtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/arroon(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators6arroon_6periodSi_AA12ArroonResultVtSayxG_SitAA8QuotableRzlF">arroon(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Aroon</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">arroon</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="kt"><a href="Structs/ArroonResult.html">ArroonResult</a></span><span class="p">)</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators8aroonosc_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/aroonosc(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators8aroonosc_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">aroonosc(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Aroon Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">aroonosc</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4asinySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/asin(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4asinySi_SaySdGtACF">asin(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Arcsine</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">asin</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4atanySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/atan(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4atanySi_SaySdGtACF">atan(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Arctangent</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">atan</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3atr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/atr(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3atr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">atr(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Average True Range</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">atr</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators8avgpriceySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/avgprice(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators8avgpriceySi_SaySdGtSayxGAA8QuotableRzlF">avgprice(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Average Price</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">avgprice</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3bopySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/bop(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3bopySi_SaySdGtSayxGAA8QuotableRzlF">bop(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Balance of Power</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">bop</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3cci_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/cci(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3cci_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">cci(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Commodity Channel Index</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">cci</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4ceilySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/ceil(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4ceilySi_SaySdGtACF">ceil(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Ceiling</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">ceil</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3cmo_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/cmo(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3cmo_6periodSi_SaySdGtAD_SitF">cmo(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Chande Momentum Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">cmo</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3cosySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/cos(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3cosySi_SaySdGtACF">cos(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Cosine</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">cos</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4coshySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/cosh(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4coshySi_SaySdGtACF">cosh(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Hyperbolic Cosine</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">cosh</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators8crossany1a1bSi_SaySdGtAE_AEtF"></a>
                    <a name="//apple_ref/swift/Function/crossany(a:b:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators8crossany1a1bSi_SaySdGtAE_AEtF">crossany(a:b:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Crossany</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">crossany</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="nv">b</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>a</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>A values</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>b</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>B values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators9crossover1a1bSi_SaySdGtAE_AEtF"></a>
                    <a name="//apple_ref/swift/Function/crossover(a:b:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators9crossover1a1bSi_SaySdGtAE_AEtF">crossover(a:b:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Crossover</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">crossover</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="nv">b</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>a</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>A values</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>b</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>B values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3cvi_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/cvi(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3cvi_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">cvi(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Chaikins Volatility</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">cvi</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5decay_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/decay(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5decay_6periodSi_SaySdGtAD_SitF">decay(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Linear Decay</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">decay</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators2di_6periodSi_AA9DirectionVtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/di(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators2di_6periodSi_AA9DirectionVtSayxG_SitAA8QuotableRzlF">di(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Directional indicator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">di</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="kt"><a href="Structs/Direction.html">Direction</a></span><span class="p">)</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period n</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3divySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/div(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3divySi_SaySdGtACF">div(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector division</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">div</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators2dm_6periodSi_AA9DirectionVtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/dm(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators2dm_6periodSi_AA9DirectionVtSayxG_SitAA8QuotableRzlF">dm(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Directional Movement</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">dm</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="kt"><a href="Structs/Direction.html">Direction</a></span><span class="p">)</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period n</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3dpo_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/dpo(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3dpo_6periodSi_SaySdGtAD_SitF">dpo(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Detrended Price Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">dpo</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators2dx_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/dx(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators2dx_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">dx(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Directional Movement Index</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">dx</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators6edecay_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/edecay(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators6edecay_6periodSi_SaySdGtAD_SitF">edecay(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Exponential Decay</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">edecay</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3emvySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/emv(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3emvySi_SaySdGtSayxGAA8QuotableRzlF">emv(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Ease of Movement</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">emv</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3expySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/exp(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3expySi_SaySdGtACF">exp(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Exponential</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">exp</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators6fisher_6periodSi_AA12FisherResultVtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/fisher(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators6fisher_6periodSi_AA12FisherResultVtSayxG_SitAA8QuotableRzlF">fisher(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Fisher Transform</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">fisher</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="kt"><a href="Structs/FisherResult.html">FisherResult</a></span><span class="p">)</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5floorySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/floor(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5floorySi_SaySdGtACF">floor(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Floor</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">floor</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4fosc_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/fosc(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4fosc_6periodSi_SaySdGtAD_SitF">fosc(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Forecast Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">fosc</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3hma_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/hma(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3hma_6periodSi_SaySdGtAD_SitF">hma(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Hull Moving Average</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">hma</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3kvo_5short4longSi_SaySdGtSayxG_S2itAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/kvo(_:short:long:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3kvo_5short4longSi_SaySdGtSayxG_S2itAA8QuotableRzlF">kvo(_:short:long:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Klinger Volume Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">kvo</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="nv">short</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">long</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>short</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The short period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>long</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The long period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3lag_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/lag(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3lag_6periodSi_SaySdGtAD_SitF">lag(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Lag</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">lag</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators6linreg_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/linreg(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators6linreg_6periodSi_SaySdGtAD_SitF">linreg(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Linear Regression</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">linreg</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators15linregintercept_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/linregintercept(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators15linregintercept_6periodSi_SaySdGtAD_SitF">linregintercept(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Linear Regression Intercept</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">linregintercept</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators11linregslope_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/linregslope(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators11linregslope_6periodSi_SaySdGtAD_SitF">linregslope(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Linear Regression Slope</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">linregslope</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators2lnySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/ln(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators2lnySi_SaySdGtACF">ln(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Natural Log</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">ln</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5log10ySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/log10(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5log10ySi_SaySdGtACF">log10(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Base-10 Log</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">log10</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4macd_5short4long6signalSi_AA10MACDResultVtSaySdG_S3itF"></a>
                    <a name="//apple_ref/swift/Function/macd(_:short:long:signal:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4macd_5short4long6signalSi_AA10MACDResultVtSaySdG_S3itF">macd(_:short:long:signal:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Moving Average Convergence/Divergence</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">macd</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="nv">short</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">long</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">signal</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="kt"><a href="Structs/MACDResult.html">MACDResult</a></span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs values</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>short</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The short period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>long</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The long period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>signal</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The signal period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators8marketfiySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/marketfi(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators8marketfiySi_SaySdGtSayxGAA8QuotableRzlF">marketfi(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Market Facilitation Index</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">marketfi</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4mass_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/mass(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4mass_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">mass(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Mass Index</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">mass</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3max_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/max(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3max_6periodSi_SaySdGtAD_SitF">max(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Maximum In Period</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">max</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators2md_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/md(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators2md_6periodSi_SaySdGtAD_SitF">md(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Mean Deviation Over Period</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">md</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators8medpriceySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/medprice(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators8medpriceySi_SaySdGtSayxGAA8QuotableRzlF">medprice(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Median Price</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">medprice</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3mfi_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/mfi(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3mfi_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">mfi(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Money Flow Index</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">mfi</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3mom_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/mom(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3mom_6periodSi_SaySdGtAD_SitF">mom(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Momentum</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">mom</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3msw_6periodSi_AA9MSWResultVtSaySdG_SitF"></a>
                    <a name="//apple_ref/swift/Function/msw(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3msw_6periodSi_AA9MSWResultVtSaySdG_SitF">msw(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Mesa Sine Wave</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">msw</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="kt"><a href="Structs/MSWResult.html">MSWResult</a></span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3mulySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/mul(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3mulySi_SaySdGtACF">mul(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Multiplication</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">mul</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4natr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/natr(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4natr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">natr(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Normalized Average True Range</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">natr</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3nvi_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/nvi(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3nvi_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">nvi(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Normalized Average True Range</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">nvi</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3obvySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/obv(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3obvySi_SaySdGtSayxGAA8QuotableRzlF">obv(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>On Balance Volume</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">obv</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3ppo_5short4longSi_SaySdGtAE_S2itF"></a>
                    <a name="//apple_ref/swift/Function/ppo(_:short:long:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3ppo_5short4longSi_SaySdGtAE_S2itF">ppo(_:short:long:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Percentage Price Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">ppo</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="nv">short</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">long</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4psar_12acceleration0C3MaxSi_SaySdGtSayxG_S2dtAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/psar(_:acceleration:accelerationMax:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4psar_12acceleration0C3MaxSi_SaySdGtSayxG_S2dtAA8QuotableRzlF">psar(_:acceleration:accelerationMax:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Parabolic SAR</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">psar</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="nv">acceleration</span><span class="p">:</span> <span class="kt">Double</span><span class="p">,</span> <span class="nv">accelerationMax</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>acceleration</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The acceleration factor</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>accelerationMax</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The accelation factor maximum</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3pviySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/pvi(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3pviySi_SaySdGtSayxGAA8QuotableRzlF">pvi(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Positive Volume Index</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">pvi</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators6qstick_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/qstick(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators6qstick_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">qstick(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Qstick</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">qstick</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>period</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3roc_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/roc(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3roc_6periodSi_SaySdGtAD_SitF">roc(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Rate of Change</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">roc</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4rocr_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/rocr(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4rocr_6periodSi_SaySdGtAD_SitF">rocr(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Rate of Change Ratio</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">rocr</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5roundySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/round(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5roundySi_SaySdGtACF">round(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Round</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">round</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3rsi_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/rsi(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3rsi_6periodSi_SaySdGtAD_SitF">rsi(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Relative Strength Index</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">rsi</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3sinySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/sin(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3sinySi_SaySdGtACF">sin(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Sine</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">sin</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4sinhySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/sinh(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4sinhySi_SaySdGtACF">sinh(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Hyperbolic Sine</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">sinh</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4sqrtySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/sqrt(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4sqrtySi_SaySdGtACF">sqrt(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Sqrt</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">sqrt</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators6stddev_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/stddev(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators6stddev_6periodSi_SaySdGtAD_SitF">stddev(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Standard Deviation Over Period</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">stddev</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators6stderr_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/stderr(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators6stderr_6periodSi_SaySdGtAD_SitF">stderr(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Standard Error Over Period</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">stderr</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5stoch_7kPeriod08kSlowingC001dC0Si_AA11StochResultVtSayxG_S3itAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/stoch(_:kPeriod:kSlowingPeriod:dPeriod:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5stoch_7kPeriod08kSlowingC001dC0Si_AA11StochResultVtSayxG_S3itAA8QuotableRzlF">stoch(_:kPeriod:kSlowingPeriod:dPeriod:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Stochastic Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">stoch</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="nv">kPeriod</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">kSlowingPeriod</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">dPeriod</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="kt"><a href="Structs/StochResult.html">StochResult</a></span><span class="p">)</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>period</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators8stochrsi_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/stochrsi(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators8stochrsi_6periodSi_SaySdGtAD_SitF">stochrsi(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Stochastic RSI</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">stochrsi</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3sub1a1bSi_SaySdGtAE_AEtF"></a>
                    <a name="//apple_ref/swift/Function/sub(a:b:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3sub1a1bSi_SaySdGtAE_AEtF">sub(a:b:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Substraction</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">sub</span><span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="nv">b</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3sum_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/sum(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3sum_6periodSi_SaySdGtAD_SitF">sum(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Sum Over Period</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">sum</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3tanySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/tan(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3tanySi_SaySdGtACF">tan(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Tangent</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">tan</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4tanhySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/tanh(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4tanhySi_SaySdGtACF">tanh(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Hyperbolic Tangent</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">tanh</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5todegySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/todeg(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5todegySi_SaySdGtACF">todeg(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Degree Conversion</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">todeg</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5toradySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/torad(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5toradySi_SaySdGtACF">torad(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Radian Conversion</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">torad</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators2trySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/tr(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators2trySi_SaySdGtSayxGAA8QuotableRzlF">tr(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>True Range</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">tr</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4trix_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/trix(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4trix_6periodSi_SaySdGtAD_SitF">trix(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Trix</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">trix</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5truncySi_SaySdGtACF"></a>
                    <a name="//apple_ref/swift/Function/trunc(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5truncySi_SaySdGtACF">trunc(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vector Truncate</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">trunc</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3tsf_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/tsf(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3tsf_6periodSi_SaySdGtAD_SitF">tsf(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Time Series Forecast</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">tsf</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements.</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators8typpriceySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/typprice(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators8typpriceySi_SaySdGtSayxGAA8QuotableRzlF">typprice(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Typical Price</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">typprice</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators6ultosc_5short6medium4longSi_SaySdGtSayxG_S3itAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/ultosc(_:short:medium:long:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators6ultosc_5short6medium4longSi_SaySdGtSayxG_S3itAA8QuotableRzlF">ultosc(_:short:medium:long:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Ultimate Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">ultosc</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="nv">short</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">medium</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">long</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>short</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The short period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>medium</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The medium period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>long</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The long period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators8variance_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/variance(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators8variance_6periodSi_SaySdGtAD_SitF">variance(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Variance Over Period</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">variance</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3vhf_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/vhf(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3vhf_6periodSi_SaySdGtAD_SitF">vhf(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Vertical Horizontal Filter</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">vhf</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5vidya_5short4long5alphaSi_SaySdGtAF_S2iSdtF"></a>
                    <a name="//apple_ref/swift/Function/vidya(_:short:long:alpha:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5vidya_5short4long5alphaSi_SaySdGtAF_S2iSdtF">vidya(_:short:long:alpha:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Variable Index Dynamic Average</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">vidya</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="nv">short</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">long</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">alpha</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>short</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The short period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>long</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The long period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>alpha</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The alpha value</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators10volatility_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/volatility(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators10volatility_6periodSi_SaySdGtAD_SitF">volatility(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Annualized Historical Volatility</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">volatility</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4vosc_5short4longSi_SaySdGtSayxG_S2itAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/vosc(_:short:long:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4vosc_5short4longSi_SaySdGtSayxG_S2itAA8QuotableRzlF">vosc(_:short:long:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Volume Oscillator</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">vosc</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="nv">short</span><span class="p">:</span> <span class="kt">Int</span><span class="p">,</span> <span class="nv">long</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>short</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The short period</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>long</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The long period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators4vwma_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/vwma(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators4vwma_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">vwma(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Volume Weighted Moving Average</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">vwma</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators3wadySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/wad(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators3wadySi_SaySdGtSayxGAA8QuotableRzlF">wad(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Williams Accumulation/Distribution</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">wad</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators7wcpriceySi_SaySdGtSayxGAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/wcprice(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators7wcpriceySi_SaySdGtSayxGAA8QuotableRzlF">wcprice(_:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Weighted Close Price</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">wcprice</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators7wilders_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/wilders(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators7wilders_6periodSi_SaySdGtAD_SitF">wilders(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Wilders Smoothing</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">wilders</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The input values</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5willr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF"></a>
                    <a name="//apple_ref/swift/Function/willr(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5willr_6periodSi_SaySdGtSayxG_SitAA8QuotableRzlF">willr(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Weighted Close Price</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="n">willr</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">T</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt"><a href="Protocols/Quotable.html">Quotable</a></span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>An array of <code><a href="Protocols/Quotable.html">Quotable</a></code> elements</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:15tulipindicators5zlema_6periodSi_SaySdGtAD_SitF"></a>
                    <a name="//apple_ref/swift/Function/zlema(_:period:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:15tulipindicators5zlema_6periodSi_SaySdGtAD_SitF">zlema(_:period:)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Zero-Lag Exponential Moving Average</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">zlema</span><span class="p">(</span><span class="n">_</span> <span class="nv">inputs</span><span class="p">:</span> <span class="p">[</span><span class="kt">Double</span><span class="p">],</span> <span class="n">period</span> <span class="nv">n</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="kt">Int</span><span class="p">,</span> <span class="p">[</span><span class="kt">Double</span><span class="p">])</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Parameters</h4>
                        <table class="graybox">
                          <tbody>
                            <tr>
                              <td>
                                <code>
                                <em>inputs</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The inputs</p>
                                </div>
                              </td>
                            </tr>
                            <tr>
                              <td>
                                <code>
                                <em>n</em>
                                </code>
                              </td>
                              <td>
                                <div>
                                  <p>The period</p>
                                </div>
                              </td>
                            </tr>
                          </tbody>
                        </table>
                      </div>
                    </section>
                  </div>
                </li>
              </ul>
            </div>
          </section>
        </section>
        <section id="footer">
          <p>&copy; 2019 <a class="link" href="https://blog.yageek.net" target="_blank" rel="external">Yannick Heinrich</a>. All rights reserved. (Last updated: 2019-06-11)</p>
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